#Exercicio 8.1

eutad <- read.table("palmadulto.txt", sep = "")

eutad <- eutad[-1, ]

eutad


dist=matrix(NA, ncol=102, nrow=102)


for(i in 1:101)
  
{
  for(j in (i+1):102)
  {
    difx2=(eutad$V3[i]-eutad$V3[j])^2
    dify2=(eutad$V4[i]-eutad$V4[j])^2
    dist[i,j]<-sqrt(difx2 + dify2)
    dist[j,i]<-sqrt(difx2 + dify2)
  }       
}

(nn<-apply(dist, 1, min, na.rm=TRUE))

(mnn<-mean(nn))



#simulaao de tomadas

resultado=rep(NA, 1000)

resultado[1]=mnn

for(w in 2:1000)
{
  xsim=sample(runif(102,0,320))
  ysim=sample(runif(102,0,320))
  matriz.xy=matrix(NA, ncol=102, nrow=102)
  
  for(i in 1:101)
  {
    for(j in (i+1):102)
    {
      difx2=(xsim[i]-xsim[j])^2
      dify2=(ysim[i]-ysim[j])^2
      matriz.xy[i,j]<-sqrt(difx2 + dify2)
      matriz.xy[j,i]<-sqrt(difx2 + dify2)
    }
  }
  
 
  resultado[w]=mean(apply(matriz.xy, 1, min, na.rm = TRUE))	
}

resultado <- resultado[-1]

#histograma do resultado
print(hist(resultado))

a = resultado[1]

media=mean(resultado)

b = media+(media-a)

abline(v = a, col="red")

abline(v=b, col="red")

calc = sum(resultado<=a|resultado>=b)

probabilidade = bic/length(resultado)

##############################################################################

#Exercicio 8.2.

massa <- read.csv ("massa.txt", sep = ";", dec = ",")
head(massa)


which(is.na(mass$brain))

massa <- massa[-c(which(is.na(massa$brain))),]

# 2.1
massa$logbody <- log(massa$body)
massa$logbrain <- log(massa$brain)
mod1 <- lm(massa$logbrain~massa$logbody)
b <- coefficients(mod1)[[2]]

# 2.2
sim_b <- rep(NA, 2000)

sim_b[1] <- b

# 2.3 , 2.4., 2.5.
for (i in 2:2000)
{
  sim_brain <- sample(massa$brain)
  sim_b[i] <- coefficients(lm(log(sim_brain)~massa$logbody))[[2]] 
  
} 

# 2.6
hist(sim_b)

abline(v = b, col = "red")

bicaudal <- sum(abs(sim_b)>=abs(b))
bicaudal
length(sim_b)
p.bi = bicaudal/length(sim_b)
p.bi

print("A probilidade  muito baixa (p.bi = 5e-04), logo, conclui-se que as variveis so dependentes.")

